1. Field of the Invention
The present invention relates to a method and apparatus for controlling a rolling mill for rolling a rolled sheet of a metal or the like and, more particularly, to a method and apparatus for controlling operation amounts supplied to actuators respectively arranged in work and drive sides of the rolling mill to adjust the sheet flatness or sheet crown of the rolled sheet.
2. Description of the Related Art
In recent years, various market needs for hot and cold rolling sheet plates and surface treated steel sheets have arisen in terms of not only mass production but also quality improvements and shortening of delivery due. In order to immediately satisfy these market needs, various methods of controlling rolling mills have been proposed.
Of these methods, a recent control method is disclosed in "Method of Controlling Shape of Rolled Sheet", Nihon Kokan Giho No. 122, 1989. This method associated with control of the sheet flatness of rolled sheets. More specifically, a detected shape of a rolled sheet is represented by a function f(x) normalized in a direction of sheet width and is approximated by an orthonormal function .PHI..sub.i (x) of a maximum of the sixth degree as follows: ##EQU1## where x is the position in the direction of sheet width, satisfying condition -1.ltoreq.x .ltoreq.1, and ##EQU2## are terms of a degree equal to or higher than the sixth degree.
If a change in shape by an operation amount .DELTA.J.sub.j of a shape control device j is defined as .DELTA.F.sub.j (x), a predicted shape obtained upon operation of n devices by a predetermined amount is represented by equation (2) below: ##EQU3##
An evaluation function in shape control is given by equation (3) when a target shape is represented as f(x): ##EQU4##
A minimum value of the evaluation function is obtained by .DELTA.J.sub.j obtained by equation (4) below: EQU .PHI./.DELTA.J.sub.j =O (j=1 to n) (4)
In this case, by giving (.differential.F/.differential.J).sub.j, simultaneous equations (4) are solved to obtain a control output of each shape control device.
Coarse control is performed by the above output determining scheme, and remaining amounts, i.e., values of the sixth or higher degrees in equation (1) are corrected by fine control.
As described above, conventional flatness control of a rolled sheet is performed in the range of -1.ltoreq..times..ltoreq.1, i.e., in the entire width. That is, the conventional flatness control collectively performs operations throughout the width of the sheet.
In a rolled sheet actually rolled by a rolling mill, the sheet flatness or sheet crown of a portion extending from the center to a work side (WS) of the sheet is not necessarily symmetrical with that from the center to a drive side (DS) of the sheet, thereby degrading precision of flatness and crown control. This drawback typically occurs in particularly wide rolled sheets.
In recent years, strong demand has arisen for improving quality (yield) of wide rolled sheets (i.e., rolled sheets having widths of about 1,000 to 2,000 mm).
In the conventional method of controlling the rolling mill, since control is collectively performed throughout the entire width of the sheet, the sheet flatness or sheet crown of the rolled sheet cannot be controlled with high precision.